LINR 1 | Lesson 1 | Making Connections (Tables)

Making Connections

 Tables

How can you use the pattern’s table to find the slope?

  • When a table represents a linear pattern, the slope can be found by computing the ratio of the change in \(y\) and the change in \(x\).
  • One way to compute the slope in linear tables is to order the \(x\)-values so that they increase by equal increments.  When arranged in this manner, the change in the \(x\)-values and the \(y\)-values can be computed and used in the ratio to determine slope.

The computation for the slope for Pattern 1 is shown in the table below where x represents the step and y represents the number of squares in that step. Tables are created using Desmos.com.

Pattern 1 Table

  \[slope=\frac{\Delta y}{\Delta x} =\frac {rise}{run}=\frac {+2}{+1}=2\]

  • Another way to compute the slope from a table is to choose any two points and compute the ratio of the change in \(y\) and the change in \(x\) between these two points.  
    • For example, choosing the points \((1,6)\) and \((4,12)\) from the table above, we can find the change in \(y\) and the change in \(x\):

\[slope=\frac{\Delta y}{\Delta x}=\frac{(12-6)}{(4-1)}=\frac {6}{3}=2\]

  • This method defines the formula for finding slope between any two points on a line where the first point is defined as \((x_1,y_1)\) and the second point is defined as \((x_2,y_2)\):  \[slope=\frac{(y_2-y_1)}{(x_2-x_1)}\]

  1. Compute the slope for the remaining patterns by ordering the \(x\)-values in each table or by choosing two points and using the slope formula.


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